We want to evaluate the optimization performance of QAOA and QAMPA in terms of their value as a \(\mathtt {WeightedMaxCutGSP}\)  solver. The metric we use is related to a goal of running the algorithm to discover as quickly as possible a bitstring associated to a sufficiently good value (as determined by a pre-defined quality threshold [1]}) of the objective function. To address this goal, our target performance metric will be the expected value of the objective function when the best result in \(R\)  runs is selected [2]}:
\(\langle \mathrm {BEST}_R\rangle = \sum _{k\in \mathcal {F}} \epsilon _k \left[\left(1- F(\epsilon _{k-1})\right)^R - \left(1-F(\epsilon _k)\right)^R \right],\) 
